A function collection for working with angles
Last updated 2 years ago by infusion .
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Angles.js is a collection of functions to work with angles. The aim is to have a fast and correct library, which can effortlessly convert between different units and can seamlessly work within different units. The result is a static library, which works on a configurable scale.


var angles = require('angles');
angles.SCALE = 360;
console.log(angles.normalize(365)); // 5
console.log(angles.normalize(-365)); // 355

Simply calculate the linear interpolation of the smaller angle.

var a = -30; // 330°
var b = 30;
var pct = 0.5; // Percentage between a and b

angles.SCALE = 360;

var dir = angles.shortestDirection(a, b); // -1 => Rotate CCW

console.log(angles.lerp(a, b, pct, dir)); // => 0

Having the scale configurable opens a lot of possibilities, like calculating clock-angles:

angles.SCALE = 60;
var time = new Date;
var s = time.getSeconds();
var m = time.getMinutes();
var h = time.getHours() / 23 * 59;
console.log(angles.between(s, m, h)); // true or false, if seconds clockhand is between the minutes and hours clockhand



Normalizes an angle to be in the interval [-180, 180), if SCALE is 360 or [-π, π) if SCALE is 2π.


Normalizes an angle to be in the interval [0, 360), if SCALE is 360 or [0, 2π) if SCALE is 2π.

shortestDirection(from, to)

Determines what the shortest rotation direction is to go from one angle to another. The result is positive if it's clock-wise.

between(n, a, b)

Determines if an angle n is between two other angles a, b. The angles don't have to be normalized.

diff(a, b)

Calculates the angular difference between two angles

lerp(a, b, p[, dir=-1])

Calculates the linear interpolation of two angles

distance(a, b)

Calculate the minimal distance between two angles


Calculate radians from current angle (Unit 2PI)


Calculate degrees from current angle (Unit 360)


Calculate gons from current angle (Unit 400)

fromSlope(p1, p2)

Calculates the angle between the x-axis and the line formed by two points.

fromSinCos(sin, cos)

Calculates the original angle (in full resolution) based on the sine and co-sine of the angle.

quadrant(x, y[k=4[, shift=0]])

Calculates the quadrant (with k=4, or octant with k=8) in which a point with coordinates x,y falls. Optionally, the coordinate system can be rotated with the shift parameter, which follows the SCALE-attribute. A positive value rotates counter-clockwise.


Translates the angle to a point of the compass ("N", "NE", "E", "SE", "S", "SW", "W", "NW") in the normal windrose way (N=0, E=90, S=180, W=270). If you want to want to have the major directions only, remove every second element from the array DIRECTIONS.


Installing Angles.js is as easy as cloning this repo or use one of the following commands:

bower install angle


npm install angles

Using Angles.js with the browser

<script src="angles.js"></script>

Using Angles.js with require.js

<script src="require.js"></script>
function(Angles) {

Coding Style

As every library I publish, Angles.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.


If you plan to enhance the library, make sure you add test cases and all the previous tests are passing. You can test the library with

npm test

Copyright and licensing

Copyright (c) 2016, Robert Eisele Dual licensed under the MIT or GPL Version 2 licenses.

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